Exact determinant and inverse calculations for yale and list 2x2 and 3x3

[translunar]

Right now exact determinant calculations are disabled for Yale and list matrices, but allowed for dense, of sizes 2x2 and 3x3. This doesn't make a ton of sense. They're all pretty trivial calculations.

Someone needs to implement an algorithm which calculates 2x2 and 3x3 exact determinants for Yale and list matrices. It goes in nm_det_exact in ruby_nmatrix.c.

Subsequently, nm_inverse_exact can be adjusted, too; however, this requires the exact determinant calculation.

[NSchock]

I am interested in this; I will give it a try.

[omegaga]

Hi @NSchock , I'm also working on this issue since yesterday but I didn't reply to it in time. I am wondering which part you are currently working on in case we do duplicate job.
Sorry for the inconvenience :(

[NSchock]

@omegaga I haven't gotten much work done yet but I'm willing to split it with you. What if one of us worked on the determinant and one of us worked on the inverse? What work have you done so far?

[omegaga]

@NSchock Sorry for not seeing that. Is inverse part partially based on det?

[omegaga]

I'm now working on Yale matrix. In 3*3 cases, I think it will be faster to transfer it into a dense matrix first, in order to avoid repetitive calculations. Is it appropriate? @MohawkJohn

[translunar]

Ah, just now seeing this message. Yes, I think transferring into a dense matrix would be appropriate, but you can do this in a single line of Ruby code instead of a few dozen lines of C/C++ code.

[spacewander]

Is it acceptable to cast yale/list matrix into dense matrix in the C code?
It's possible to implement algorithms separately for yale/list matrix, but this will make things more complex. Since we will have 3 types of stype, each has N dtype.

Currently we just support 2×2 and 3×3 matrices, so the extra cost may not be high.

[translunar]

Hey, sorry, just got back from vacation. I think it's probably preferred that casting only happen for very small matrices, and then there has to be some consideration of the trade-offs. For example, is it cheaper to cast and then calculate the determinant as a dense, or is it cheaper to simply calculate the determinant of a 3x3 yale matrix in Ruby code?

I suppose perhaps this issue is kind of a badly defined one. What we really want is determinant and inverse calculation for full Yale matrices, and for those casting would not be good (and people can already do that on their own). For list matrices, it's probably always appropriate to cast to Yale or dense first, just because of the way the data structure is laid out.